I was overwhelmed and faced with despair when that barbarian savage first attacked me. I was expanding well and had thought that I'd have the upper hand considering all the shard advantages and vision that I was given, but man was I wrong. He pushed my heroes and provinces all the way to my stronghold and left high level adventurers and horsemen guards everywhere.
The way I managed to push him back and ultimately win was this:
1. Research Tier 2 units ASAP (in my case, guardsmen)
2. Make sure Stronghold had at least 1 unit in garrison
3. Focused on leveling my heroes (in my case, Warrior and Scout) until they could consistently kill enemy heroes (I trained them till Warrior had Round Attack and Scout had Double Shot)
4. Once I can consistently beat their heroes down, I checked to see if I could easily take out the enemy's guards
5. Then, when that's all set - I wait until his heroes attack and die at my stronghold (this way they take longer to respawn and I have better chance to heal/repair/reinforce my heroes' squads), then begin conquering strategic points until I won
Since steady income was so difficult to procure, I relied mostly on quests and exploring to get bursts of cash to fuel my efforts.
I wish you the best of luck! Let us know how it goes.